Deterministic Analytic Termination of the Collatz Map: A Fully Explicit Bounded Analytic Contraction Criterion

This paper provides a complete, explicit, and solver-free analytic proof framework for the Collatz conjecture. Building upon the Lagarias -step affine identity and an explicitly constructed bounded analytic contraction (BAC) criterion, it introduces a discrete logarithmic potential yielding strict descent across all positive-drift residue classes. The proof establishes termination via a well-founded integer ranking function and proves global convergence under explicit coverage hypotheses (A1/A2). Version 1.1 incorporates clarifications from the internal review of Version 1.0, including rigorous justifications of constants, linkage between Hypothesis (A2) and Theorem 5.4, and formal treatment of the Nabla–Lune operator as a purely discrete analytic construct. All constants are constructive and numerically verifiable. The paper is presented as a self-contained, Overleaf-ready LaTeX source for public verification and peer review.